LMIs in Control/pages/Discrete Time H∞ Optimal Full State Feedback Control

Discrete-Time H∞-Optimal Full-State Feedback Control

A discrete time system operates on a discrete time signal input and produces a discrete time signal output. They are used in digital signal processing, such as digital filters for images or sound. The class of discrete time systems that are both linear and time invariant, known as discrete time LTI systems.

A full state feedback controller design for a Discrete Time system, to minimize the H∞ norm of the closed loop system with exogenous input and performance output .

The SystemEdit

Discrete-Time LTI System with state space realization  
 

The DataEdit

The matrices: System  .

The Optimization ProblemEdit

The following feasibility problem should be optimized:

  is minimized while obeying the LMI constraints.

The LMI:Edit

Discrete-Time H∞-Optimal Full-State Feedback Control

The LMI formulation

H∞ norm <  

 

Conclusion:Edit

The H∞-optimal full-state feedback gain is recovered by  

ImplementationEdit

A link to CodeOcean or other online implementation of the LMI
MATLAB Code

Related LMIsEdit

[1] - Continuous Time H∞ Optimal Full State Feedback Control

External LinksEdit

A list of references documenting and validating the LMI.

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